Traditional modeling systems operate in either the geometric domain or in the volumetric (quantized) domain. Geometric models are generally built using lines, polygons, NURBS, and the like. FIG. 1 incorporated herein shows a geometric representation of a space shuttle 100 composed of polygons. Geometric representations are excellent for modeling objects that can be characterized with simple geometric forms. However, geometric representations are not as effective for modeling more organic, realistic, and/or complex shapes.
Voxel-based models offer advantages in both graphical and haptic representation of three-dimensional objects, particularly objects having complex shapes that cannot be easily characterized with simple geometric forms such as lines, polygons, spheres, cylinders, or the like. Voxel-based models offer significant speed and other processing advantages for production of realistic force-feedback to a user in a haptic virtual reality system. However, voxel-based models are not as effective as geometric models at representing objects with sharp edges.
Traditional modeling systems do not combine both volumetric and geometric representations, and do not have the ability to perform operations in one domain (volumetric or geometric) and have the results reflected in the other domain. This restricts the utility of such modeling systems in applications that require both industrial design (e.g., design of man-made, man-altered, and/or linear forms) and organic modeling (e.g., modeling non-linear, complex forms that appear in nature).